Trump lawyer Rudy Giuliani had expressed a similar sentiment when he told the Times that while there was a discussion, the payment was never made and the tape showed that Trump had done nothing wrong.
"Inconceivable that the government would break into a lawyer's office (early in the morning) - nearly unheard of", the president tweeted.
He then said "even more inconceivable... that a lawyer would tape a client... totally unheard of and perhaps illegal".
Jonny Bairstow thinks England's ODI and Test form comparisons are 'unfair'
Rishabh Pant has received a maiden call-up while another wicket-keeper batsman Dinesh Karthik has also been included. Given Kuldeep's recent success, it will be interesting to see who gets the nod in the playing eleven.
Trump insisted on his innocence in Saturday's tweet, assuring his followers that "the good news is that your favorite President did nothing wrong!".
Michael Cohen recorded the conversation with Trump, which was seized by federal agents.
The prosecutors working on the case had not reviewed the recording because it, along with millions of other documents and files seized in Federal Bureau of Investigation searches of Cohen's home, hotel room and office in April, was undergoing the special master process, in which an independent party reviews whether the items should be regarded as privileged and thus withheld from prosecutors.
Trump blames Putin personally for election meddling in latest reversal
In a CBS interview with anchor Jeff Glor , Trump said that he held Putin "personally responsible" for the election interference. The President spoke to key lawmakers and outside confidants leading up to his remarks, people familiar with the matter said.
In May, President Trump admitted that he had reimbursed Mr Cohen for a payment to another woman to hush up her claims of an affair.
Mr Cohen, who has not been charged, is reportedly under investigation for possible bank and tax fraud, as well as potential violation of election law.
But he said no money was actually ever transferred, and the recording itself amounted to "powerful exculpatory evidence".
On the tape, Trump can be heard urging Cohen to make sure he properly documents the agreement to buy the rights and urges him to use a check - rather than cash - to keep a record of the transaction, the person said. The source also said that Cohen "is no longer taking a bullet for you (Trump), is no longer a flunky", calling his declaration of independence "his July 4th moment". CNN's Keith Allen has also just reported that Trump's reaction when he was informed that at least one tape was in the FBI's possession, was, "I can't believe Michael would do this with me". She turned down the offer and began a relationship that included, she said, interactions between the two "many dozens of times".
Trump denies wrongdoing, says lawyer's tape 'perhaps illegal'
The New York Times also said the Federal Bureau of Investigation seized the recording this year during a raid on Cohen's office. But he said no money was actually ever transferred, and the recording itself amounted to "powerful exculpatory evidence".
In the lead-up to the 2016 presidential election, Ms McDougal sold her story to the National Enquirer, which is owned by a personal friend of Mr Trump. But the agreement meant that McDougal signed a non-disclosure agreement that prevented her from revealing the affair. In New York, it is completely legal for a lawyer to tape a client.